For disc brakes and if you didn't replace the rotors, check that the pads do not ride on ANY area of the rotor that has not been resurfaced. If the noise mostly happens at low speed while _not_ applying brake, and if they are disc brakes, check for bent or misaligned abutment clips and anti-rattle clips.
If you installed them yourself did you use any of that liquid plastic stuff on the BACKS of the pads? It lightly glues them to the calipers preventing vibration.
If they are brand new discs too, they may squeak a bit until the machineing grooves get ground away... a few days driving.
Could be grease or oil on the brake pad. If so, buy some pad cleaner and follow the instructons.
A squeak is a vibration. Vibrations can be eliminated in many cases, but some cars such as the Neon are inherently noisy. All surfaces the come in contact with each other except the pad to rotor surfeace should be thoughly cleaned with a disc, abrasive paper, wire brush or similiar, including any caliper pins. Apply a coating of disc brake caliper grease to all these loactions prior to assy..
Newer brakes are no longer made with asbestos (which was found to cause cancer) so they switched to all sorts of things... but I've noticed that newer brakes are louder and they don't feel as nice when braking. Or they may need a little while to break in. If this continues, then take it back to where you had the brakes done and have them take a look. :)
If you installed them yourself, you need to check to see if your rotors are warped or uneven, this will also make a squealing sound. You may need to have your rotors turned or replaced.
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